213120000 has 330 divisors, whose sum is σ = 789761258. Its totient is φ = 55296000.

The previous prime is 213119993. The next prime is 213120029. The reversal of 213120000 is 21312.

It is a happy number.

It can be written as a sum of positive squares in 5 ways, for example, as 40144896 + 172975104 = 6336^2 + 13152^2 .

It is a Harshad number since it is a multiple of its sum of digits (9).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 29 ways as a sum of consecutive naturals, for example, 5759982 + ... + 5760018.

Almost surely, 2^213120000 is an apocalyptic number.

213120000 is a gapful number since it is divisible by the number (20) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 213120000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (394880629).

213120000 is an abundant number, since it is smaller than the sum of its proper divisors (576641258).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

213120000 is an equidigital number, since it uses as much as digits as its factorization.

213120000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 83 (or 47 counting only the distinct ones).

The product of its (nonzero) digits is 12, while the sum is 9.

The square root of 213120000 is about 14598.6300727157. The cubic root of 213120000 is about 597.3213929019.

Adding to 213120000 its reverse (21312), we get a palindrome (213141312).

Multiplying 213120000 by its reverse (21312), we get a square (4542013440000 = 2131200²).

213120000 divided by its reverse (21312) gives a 4-th power (10000 = 10⁴).

The spelling of 213120000 in words is "two hundred thirteen million, one hundred twenty thousand".